As well as being the symbol of Tyrone, the red hand is also the emblem of Ulster, where it is one of the few symbols which is embraced by both sides of the religious divide. The red hand is also the symbol of the O'Neill family.

Where does the red hand come from?

The most common story is that at http://flagspot.net/flags/gb-ni-ty.html, concerning "the war between two kings for Ulster. The kings had decided that too many had died and a peaceful solution was to have a sea race as both were fond of this sport. As the race was coming to a close the King of Tyrone, O Neill saw he was loosing and thinking of the rules, first person to put a hand on the shore would be king, he cut off his hand and threw it to the shore giving rise to the legend of the red hand of Ulster and of Tyrone. The Tyrone county name comes from the Irish Tir Eoghain which translates to Eoghain county after Eoghain O Neill, the great king of Ulster.

Slightly different version on Wikipedia:A variant famous myth recounts how Ó Neill and a man named Dermott both wished to be king of Ulster. The High King of Ireland suggested a horse race across the land. As the two came in sight of the ending point, it seemed that Dermott would win, so Ó Neill cut his hand off and threw it. It reached the goal ahead of Dermott's horse, winning for Ó Neill the crown of Ulster. The Gaelic war cry Lámh Dhearg Abu (Irish meaning- Red Hand to Victory) was forever associated with the O'Neills through the centuries.